1. Field of the Invention
This invention relates to a method of and an apparatus for measuring a three-dimensional shape of a surface to be measured such as an aspherical lens mounted to a laser printer or the like, which has a complex free-shape surface shape or shape much different from a surface shape of a spherical surface and a length ranging from a few dozen to about 30 mm, with high accuracy of a fraction of a wavelength of a laser.
2. Description of the Related Art
As a method of measuring a three-dimensional shape of a surface to be measured having a free-shape surface shape or shape, one has heretofore been known which repeats dot-coordinate measurements with a tracer or stylus to thereby obtain the whole shape. However, the present method is accompanied by a drawback that the measuring time becomes long and small flaws or the like that exist in the measuring surface, are missed (see e.g., "Correction of Aspherical-surface processed shape by Shape measuring device and Aspherical surface programming device" by Ogawa, et al, O plus E, No. 155, (1992.10), P86).
As a method free of the above drawback, one is known in principle which collectively measures the whole shape of a measuring surface by utilizing a hologram prototype corresponding to a complex free-shape surface shape and an interferometer in combination. It is, however, extremely difficult to manufacture a computer hologram required to measure a large surface extending over a several tens of mm with high accuracy. As a lens mounted to a laser printer, for example, one is known which has a lengthwise size of about 150 mm and a minimum radius of curvature of about 50 mm or below. However, if attention is given to the fact that convergent light must be emitted from a hologram and the lens is placed on an off-access basis to measure a convex surface of such a lens, then a lens size ranging from 200 mm to 250 mm or above, a hologram spatial frequency of 1500 (lines/mm) or above, and a hologram graphics-drawing accuracy of about 1/20 .mu.m are required. Under the existing circumstances, however, limitations are imposed to a size of about 70 mm and a spatial frequency of about 200 lines/mm upon manufacturing the computer hologram (see, e.g., "Aspherical surface shape measuring interferometer using CGH", by Genma, Precision Engineering Journal, vol. 56, No. 10, (1990), p.1791).
As disclosed in, for example, Japanese Published Unexamined Patent Application No. 62-126305 as a method of solving the above problems, a shape measuring method is known which divides a surface to be measured into a plurality of partial regions measurable by an interferometer and joins measured data on surface shapes of the respective partial regions, which have been measured by the interferometer, to thereby obtain the whole shape of the measuring surface. According to the shape measuring method described in Japanese Published Unexamined Patent Application No. 62-126305, however, since the measuring surface is moved along the optical axis of the interferometer and measured in radial division shape, only the measuring surface having the shapes symmetric with the optical axis thereof could be measured.
As a method of dividing a measuring surface having shapes other axisymmetric shapes into regions to thereby measure a shape, a shape measuring method disclosed in, for example, Japanese Published Unexamined Patent Application No. 04-290907 is known. According to the present shape measuring method, however, the surface to be measured corresponds only to a shape extremely close to the plane.
There is also known a shape measuring method disclosed in Japanese Published Unexamined Patent Application No. 02-259509. According to the present shape measuring method, a surface to be measured is divided into a plurality of partial regions having overlapped regions measurable by an interferometer. Measured data on one surface shape is translated or rotatably moved so that the amount of displacement in measured data on two surface shapes sharing the use of an overlapped region is minimized, to join measured data on surface shapes measured for the respective partial regions to each other by fitting, whereby the whole shape of the surface to be measured is obtained. However, the present shape measuring method has a drawback in that the accuracy of fitting is not sufficiently obtained depending on the shape or size of the overlapped region.
A method proposed by Japanese Patent Application No. 8-27073 filed by the present inventors is known to make up for the above drawback. Japanese Patent Application No. 8-27073 is originally intended for cross-sectional shapes. However, since the present method can be applied to three-dimensional shape instrumentation using an interferometer as described in its embodiment, the method applied to the three-dimensional shape instrumentation will be explained herein. This method is one wherein the amount of displacement or movement required to join respective partial regions to each other is considered to be divided into XYZ axial directions and six components extending in the direction of rotation with respective axes as the centers, the accuracy of fitting using each overlapped region is compared with the accuracy of each of stages for determining positional attitudes of the interferometer and the respective partial regions every six components, and measured data on surface shapes measured for the respective partial regions are joined to one another using values each having better accuracy. Thus, this method has also such drawbacks as will be described below. Although the accuracy has been improved, the required accuracy has not yet been achieved.
Since the hologram prototype is insufficient in accuracy as has already been described, freedom of way is virtually limited to using the spherical or plane prototype to realize the measurement of high accuracy by the interferometer. However, when the complex free-shape surface shape or shape is measured using the spherical or plane prototype, a range measurable at a time becomes extremely small. A range measurable by the plane prototype is considered to be about 2 mm.times.2 mm at most, for example. Therefore, the regions that overlap among the respective partial regions, become small and the accuracy is not sufficiently obtained in the case of the fitting using the conventional overlapped regions.
It is essential that the stages for respectively determining the positional attitudes of the interferometer and the respective partial regions include the rotatable axis as well as the translational axis to measure the complex free-shape surface shape. The accuracy of the stage including the rotatable axis has its limitation because an Abbe's error corresponding to the primary error due to inability to measure the length by the same axis is produced in proportion to the maximum length of an object to be measured.
Thus, even if the method proposed by Japanese Patent Application No. 8-27073 is used, a problem arose in that the measured data on the surface shapes measured for the respective partial regions could not be eventually joined to one another with high accuracy.